杂交边界点方法求解动态断裂力学问题  

Hybrid boundary node method for dynamic fracture mechanics problem

作　　者：苗雨[1] 危保明[1] 李竟成[1] 

机构地区：[1]华中科技大学土木工程与力学学院,武汉430074

出　　处：《岩土力学》2009年第7期2153-2157,共5页Rock and Soil Mechanics

基　　金：国家自然科学基金资助(No50808090)

摘　　要：结合杂交边界点法和双互易法则,推导出求解动力问题的纯边界类型无网格方法——双互易杂交边界点方法,并将该方法用于求解含中心裂纹的方板受瞬态载荷作用的问题。该方法将问题的解分为通解和特解两部分,通解使用杂交边界点法求解,特解则利用局部径向基函数近似,域内布点仅仅为了径向基插值,因此仍然是一种纯边界类型的无网格方法。同时,将移动最小二乘近似中的基函数扩充,使该方法能更好地模拟裂纹尖端应力场的奇异性,具有后处理简单、精度高的优点。数值算例表明了该方法的稳定性和有效性。Combining the hybrid boundary node method （HBNM） and the dual reciprocity principle, a truly boundary-type meshless method- dual reciprocity hybrid boundary node method is presented for solving dynamic problems. It is used to numerically find the solutions of a crack of finite specimen under an impact load. The solution is divided into particular solution and general solution. The general solution is solved by means of HBNM; and the particular solution is approximated by using radial basis functions （RBF）. The inner nodes are just for RBF interpolation, which is not influence that the present method is a boundary-only method. The basis functions enrichment in moving least squares （MLS） are presented for simulating the singularity of the stress field on the tip of the fracture. The presented method has many advantages such as simple post processing and higher accuracy. Numerical examples have shown the stability and the validity of the presented method.

关 键 词：杂交边界点法 双互易法则 动态断裂 基函数扩充 移动最小二乘 

分 类 号：O241.6[理学—计算数学]